Assume $G$,$\hat{G}$ are both free group of rank $n$,and $H$,$\hat{H}$ be their subgroups of index $k$ respectively,$h:H \rightarrow G$, $\hat{h}:\hat{H} \rightarrow\hat{G}$, are two epimorphisms. We call the triple $(H,G,h)$ and $(\hat{H},\hat{G},\hat{h})$ are equivalent if there is a isomorphism $\alpha:G \rightarrow \hat{G}$ satisfies (a)$\alpha(G)=\hat{G}$,$\alpha(H)=\hat{H}$ (b)$\alpha \circ h(x)=\hat{h} \circ \alpha(x)$,$\forall x \in H$ (1)Then I have three questions:(1)when are $(H,G,h)$ and $(\hat{H},\hat{G},\hat{h})$ equivalent?

(2)If we already know $(H,G,h)$ and $(\hat{H},\hat{G},\hat{h})$ are equivalent, how can we find an $\alpha$ ?

(3)For given $n$ and $k$,Can we give a classfy of all those triples in this way?

For all the questions above, I have considered simple the case $n=3$ and founded it's really difficulty for me. I don't know whether this question is trivial or not in Group Theory. If you can give me some useful advices i will be gratiful. Thanks!